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st: Intraclass correlation and binary hierarchical models

From   "Levy, Douglas E., Ph.D." <[email protected]>
To   <[email protected]>
Subject   st: Intraclass correlation and binary hierarchical models
Date   Wed, 11 Nov 2009 15:07:28 -0500

Hi All,

This is partly a stats question, partly a Stata question. I have binary outcome
data and I'm interested in calculating intraclass correlation for a
multilevel/hierarchical model that is nested as follows: patients within
hospitals within regions. I want to know what proportion of the variance in
outcomes resides at each level of hierarchy to help direct quality control

If my data were linear, I could run:
xtmixed Y || region: || hospital:, variance
I would add up the region, hospital, and residual variances, and see what
fraction of the total variance resided at each level.

If I had binary data and only had two levels of hierarchy, say hospital and
patient, I could run xtlogit:
xtlogit Y, re i(hospital)
and the rho statistic would be my estimate of intraclass correlation (am I
correct here?).

The "correct" model to run with my binary outcome data would be:
xtmelogit Y || region: || hospital:, variance
but this only reports the variance for region and hospital. There is no residual
variance reported to estimate the total variance (which I suppose makes sense
with binary data), and Stata does not report a level-specific rho as it does
with xtlogit.

I'd be grateful for the group's thoughts on how to tackle this issue
statistically and/or with respect to Stata.


[My apologies if this has appeared as a repost. I have tried to post this
message several times but I have not seen appear on the list.] 

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